Semantics is another word for
meaning.
In the study of language, the distinction between syntax and semantics is crucial.
In mathematics, the syntax and semantics of languages
can be defined formally. The semantics is usually defined in terms of another language.
In principle, this leads to infinite regress.
Therefore, defining semantics is basically a translation. If languages
differ in expressive power,
a meaning-preserving two-way translation is impossible.